Can you see why we will revisit this symmetry in

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Unformatted text preview: ve that the price is decreasing at a rate of $1.50 per PortaBoy sold. (Said differently, you can sell one more PortaBoy for every $1.50 drop in price.) 4. To determine the price which will move 150 PortaBoys, we find p(150) = −1.5(150)+250 = 25. That is, the price would have to be $25. 5. If the price of a PortaBoy were set at $150, we have p(x) = 150, or, −1.5x+250 = 150. Solving, we get −1.5x = −100 or x = 66.6. This means you would be able to sell 66 PortaBoys a week if the price were $150 per system. Not all real-world phenomena can be modeled using linear functions. Nevertheless, it is possible to use the concept of slope to help analyze non-linear functions using the following: Definition 2.3. Let f be a function defined on the interval [a, b]. The average rate of change of f over [a, b] is defined as: ∆f f (b) − f (a) = ∆x b−a Geometrically, if we have the graph of y = f (x), the average rate of change over [a, b] is the slope of the line which connects (a, f (a)) and (b, f (b)). This is called the sec...
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